{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a1a5d379",
   "metadata": {},
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Statistical Expectation Demonstration\n",
    "\n",
    "### Using Statistical Expectation to Model the Mathematical Operators with Random Variables Tutorial\n",
    "\n",
    "* demonstrate various mathematical operations for statistical expectation with distributions\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1) | [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy)\n",
    "\n",
    "#### Statistical Expectation\n",
    "\n",
    "Defined as a probability weighted average, **statistical expectation** is a powerful concept in statistics. It is used for:\n",
    "\n",
    "* ANOVA (analysis of variance)\n",
    "* nested variogram modeling\n",
    "* trend and residual modeling for nonstationary phenomenon\n",
    "* decion making (expected net present value)\n",
    "\n",
    "etc.\n",
    "\n",
    "To demonstrate statistical expectation the following operators will be demonstrated with random variables, distributions:\n",
    "\n",
    "* Expectation of a constant $\\longrightarrow E\\left[c\\right] = c$\n",
    "\n",
    "* Expectation of a random variable + a constant $\\longrightarrow E\\left[X + c\\right] = E\\left[X\\right] + E\\left[c\\right] = E\\left[X \\right] + c$\n",
    "\n",
    "* Expectation of the addition of two random variables $\\longrightarrow E\\left[X + Y\\right] = E\\left[X\\right] + E\\left[Y\\right]$\n",
    "\n",
    "* Expectation of the product of two random variables $\\longrightarrow E\\left[XY\\right] = E\\left[X\\right]E\\left[Y\\right]$, if $X$ and $Y$ are independent\n",
    "\n",
    "#### Objective \n",
    "\n",
    "Now that we have provided the derrivations for adding and subtracting random variables, I provide a example and demonstration with 2 random variables:\n",
    "\n",
    "* the analytical and emprical result for comparison\n",
    "* visualization of the univariate and bivariate distributions\n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python:\n",
    "\n",
    "* Install Anaconda 3 on your machine (https://www.anaconda.com/download/).  \n",
    "\n",
    "#### Load the Required Libraries\n",
    "\n",
    "The following code loads the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "64adca6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                                                # arrays\n",
    "import scipy as sp                                                # statistical distributions\n",
    "import matplotlib.pyplot as plt                                   # plotting\n",
    "import math                                                       # square root to calculate standard deviation from variance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e70318e",
   "metadata": {},
   "source": [
    "##### Specify, Sample and Visualize our Random Variables\n",
    "\n",
    "First we build a simple bivariate distribution for random varibles $X$ and $Y$. \n",
    "\n",
    "* we use the bivariate Gaussian distribution for convenience, but the derived equations for entral tendency and dispersion are general for any distribution.\n",
    "\n",
    "Then we add another uncorrelation random variable, $Z$\n",
    "\n",
    "We draw $L$ realizations from the bivariate distribution and plot the histograms and scatter plot.\n",
    "\n",
    "* below I use sample statistic instead of population statistic notation to indicate that calculation is approximative, based on a limited sample size \n",
    "\n",
    "For our demonstration:\n",
    "\n",
    "* all distributions are Gaussian, specified by mean and variance\n",
    "* X and Y are correlated (specified by covariance)\n",
    "* X and Y, Y and Z are not correlated\n",
    "\n",
    "Let's specify, sample and visualize our random variable's distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c1e8a937",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_X = 1.0; mean_Y = 0.0; mean_Z = -0.5                         # parameters for distribution\n",
    "var_X = 1.5; var_Y = 0.5; var_Z = 1.0; cov_XY = 0.8\n",
    "L = 1000                                                          # number of samples\n",
    "seed = 13\n",
    "\n",
    "np.random.seed(seed = seed)                                       # sample the random variables to visualize and check the results\n",
    "R = np.random.multivariate_normal([mean_X,mean_Y],np.array([[var_X,cov_XY],[cov_XY,var_Y]]),size=L)\n",
    "X = R[:,0]; Y = R[:,1]\n",
    "Z = np.random.normal(loc = mean_Z,scale = var_Z,size=L)\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # histogram plotting parameters\n",
    "\n",
    "plt.subplot(231)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlabel('$X$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(232)                                                   # annotated histogram of Y\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='blue',density = True,label='$Y$')\n",
    "plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--')\n",
    "plt.annotate('$E\\{Y\\}$ = ' + str(np.round(np.average(Y),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_Y$ = ' + str(np.round(np.var(Y),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$Y$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(233)                                                   # annotated scatter plot of X and Y\n",
    "plt.scatter(X,Y,color='green',alpha=0.2,edgecolor='black',s=25)\n",
    "plt.plot((np.average(X),np.average(X)),(xmin,xmax),color='goldenrod',ls='--'); plt.plot((xmin,xmax),(np.average(Y),np.average(Y)),color='mediumblue',ls='--')\n",
    "plt.xlim([xmin,xmax]); plt.ylim([xmin,xmax])\n",
    "plt.annotate(r'$C_{X,Y}$ = ' + str(np.round(np.cov(R,rowvar=False)[0,1],2)),(-4.5,3.7),fontsize = 13)\n",
    "plt.annotate(r'$\\rho_{X,Y}$ = ' + str(np.round(np.corrcoef(R,rowvar=False)[0,1],2)),(-4.5,2.6),fontsize = 13)\n",
    "plt.xlabel('$X$'); plt.ylabel('$Y$'); plt.title('$X$, $Y$ Bivariate Distribution')\n",
    "\n",
    "plt.subplot(234)                                                   # annotated histogram of X\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='grey',density = True,label='$Z$')\n",
    "plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.annotate('$E\\{Z\\}$ = ' + str(np.round(np.average(Z),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_Z$ = ' + str(np.round(np.var(Z),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlabel('$X$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$Z$ Distribution')\n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(235)                                                   # annotated scatter plot of X and Y\n",
    "plt.scatter(X,Z,color='gold',alpha=0.2,edgecolor='black',s=25)\n",
    "plt.plot((np.average(X),np.average(X)),(xmin,xmax),color='goldenrod',ls='--'); plt.plot((xmin,xmax),(np.average(Z),np.average(Z)),color='dimgrey',ls='--')\n",
    "plt.xlim([xmin,xmax]); plt.ylim([xmin,xmax])\n",
    "plt.annotate(r'$C_{X,Z}$ = ' + str(np.round(np.cov(X,Z)[0][1],2)),(-4.5,3.7),fontsize = 13)\n",
    "plt.annotate(r'$\\rho_{X,Z}$ = ' + str(np.round(np.corrcoef(X,Z)[0][1],2)),(-4.5,2.6),fontsize = 13)\n",
    "plt.xlabel('$X$'); plt.ylabel('$Z$'); plt.title('$X$, $Z$ Bivariate Distribution')\n",
    "\n",
    "plt.subplot(236)                                                   # annotated scatter plot of X and Y\n",
    "plt.scatter(Y,Z,color='darkblue',alpha=0.2,edgecolor='black',s=25)\n",
    "plt.plot((np.average(Y),np.average(Y)),(xmin,xmax),color='mediumblue',ls='--'); plt.plot((xmin,xmax),(np.average(Z),np.average(Z)),color='dimgrey',ls='--')\n",
    "plt.xlim([xmin,xmax]); plt.ylim([xmin,xmax])\n",
    "plt.annotate(r'$C_{Y,Z}$ = ' + str(np.round(np.cov(Y,Z)[0][1],2)),(-4.5,3.7),fontsize = 13)\n",
    "plt.annotate(r'$\\rho_{Y,Z}$ = ' + str(np.round(np.corrcoef(Y,Z)[0][1],2)),(-4.5,2.6),fontsize = 13)\n",
    "plt.xlabel('$Y$'); plt.ylabel('$Z$'); plt.title('$Y$, $Z$ Bivariate Distribution')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.4, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "792591c0",
   "metadata": {},
   "source": [
    "Now we can walk through various operators for random variables with expectation. \n",
    "\n",
    "* Focus on the statistical expectation operators (e.g., $E\\{X + c\\} = E\\{X \\} + c$)\n",
    "* When applicable I also show variance relations (e.g., $\\sigma^2_{X+c} = \\sigma^2_{X}$), these can be derived by expectation, but I have not added the deriviations here for brevity. \n",
    "\n",
    "#### Expectation of a random variable + a constant\n",
    "\n",
    "I demonstrate the following relationship with a random variable, $X$, and a constant, $c$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{X + c\\} = E\\{X\\} + E\\{c\\} = E\\{X \\} + c\n",
    "\\end{equation}\n",
    "\n",
    "with expectation it can also be shown that the variance will remain constant with the addition of a constant:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_{X+c} = \\sigma^2_{X}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "749b1b00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = -1.0\n",
    "X1 = X + c\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(131)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='X')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlabel('$X$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(132)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X1,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$X + c$')\n",
    "plt.vlines(np.average(X1),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$c$ = ' + str(np.round(c,2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$E\\{X+c\\}$ = ' + str(np.round(np.average(X1),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$s^2_{X+c}$ = ' + str(np.round(np.var(X1),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X + c$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(133)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X1,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$X$')\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X + c$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(X1),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$E\\{X+c\\} = E\\{X\\} + c$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{X+c} = s^2_{X}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$ and $X + c$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=0.7, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18cab60e",
   "metadata": {},
   "source": [
    "Adding a constant shift the random variable's distribution, and does not change the dispersion!\n",
    "\n",
    "#### Expectation of a product of a random variable and a constant\n",
    "\n",
    "I demonstrate the following relationship with a random variable, $Y$, and a constant, $c$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{cY\\} = cE\\{Y\\}\n",
    "\\end{equation}\n",
    "\n",
    "with expectation it can also be shown that the variance will scale as:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_{cY} = c^2 \\sigma^2_{Y}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6080c1cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 1.5\n",
    "Y2 = Y * c\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(131)                                                   # annotated histogram of X\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='blue',density = True,label='$X$')\n",
    "plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--')\n",
    "plt.annotate('$E\\{Y\\}$ = ' + str(np.round(np.average(Y),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_Y$ = ' + str(np.round(np.var(Y),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlabel('Y'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('Y Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(132)                                                   # annotated histogram of Y\n",
    "plt.hist(x=Y2,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$c \\cdot X$')\n",
    "plt.vlines(np.average(Y2),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$c$ = ' + str(np.round(c,2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$E\\{c \\cdot Y\\}$ = ' + str(np.round(np.average(Y2),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$s^2_{c \\cdot Y}$ = ' + str(np.round(np.var(Y2),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$c \\cdot Y$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(133)                                                   # annotated histogram of Y\n",
    "plt.hist(x=Y2,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$c \\cdot X$')\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='blue',density = True,label='$X$')\n",
    "plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--'); plt.vlines(np.average(Y2),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$E\\{c \\cdot Y\\} = cE\\{Y\\}$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{c \\cdot Y} = c^2 s^2_{Y}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$Y$ and $c \\cdot X$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=0.7, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4de935a5",
   "metadata": {},
   "source": [
    "if the original mean is 0, then the only result is for the variance to change, stretch or squeeze by a factor of $c^2$. The mean remains almost 0.0:\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{cY\\} = cE\\{Y\\}\n",
    "\\end{equation}\n",
    "\n",
    "if $E\\{Y\\} = 0.0$, then $cE\\{Y\\} = 0$, regardless of $c$.\n",
    "\n",
    "Let's repeat this with a random variable with a expectation not equal to 0.0, i.e., random variable, $X$, $E\\{X\\} \\ne 0.0$ and a constant, $c$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{cX\\} = cE\\{X\\}\n",
    "\\end{equation}\n",
    "\n",
    "once again, with expectation it can be shown that the variance will scale as:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_{cX} = c^2 \\sigma^2_{X}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "709d986d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = -1.2\n",
    "X2 = X * c\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(131)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlabel('X'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('X Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(132)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X2,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$c \\cdot X$')\n",
    "plt.vlines(np.average(X2),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$c$ = ' + str(np.round(c,2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$E\\{c \\cdot X\\}$ = ' + str(np.round(np.average(X2),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$s^2_{c \\cdot X}$ = ' + str(np.round(np.var(X2),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$c \\cdot X$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(133)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X2,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='red',density = True,label='$c \\cdot X$')\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(X2),0,0.6,color='darkred',ls='--')\n",
    "plt.annotate('$E\\{c \\cdot X\\} = cE\\{X\\}$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{c \\cdot X} = c^2 s^2_{X}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$ and $c \\cdot X$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=0.7, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35bc2a43",
   "metadata": {},
   "source": [
    "The constant scales the distribution, stretches or squeezes the distribution and shifts the expectation by $cE\\{X\\}$.\n",
    "\n",
    "#### Expectation of the addition of two random variables\n",
    "\n",
    "I demonstrate the following relationship for the addition of two random variables, $X$, and , $Y$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{X + Y\\} = E\\{X\\} + E\\{Y\\}\n",
    "\\end{equation}\n",
    "\n",
    "with expectation it can also be shown that the resulting variance will be:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_{X+Y} = \\sigma^2_X + \\sigma^2_Y + 2 \\cdot C_{X,Y}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ead53313",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "XY = X + Y                                                          # add 2 random variables\n",
    "XZ = Z + X\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(231)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='blue',density = True,label='$Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$E\\{Y\\}$ = ' + str(np.round(np.average(Y),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.annotate('$s^2_{Y}$ = ' + str(np.round(np.var(Y),2)),(-4.5,0.31),fontsize = 13)\n",
    "plt.annotate(r'$C_{X,Y}$ = ' + str(np.round(np.cov(R,rowvar=False)[0,1],2)),(-4.5,0.24),fontsize = 13)\n",
    "plt.xlabel('$X, Y$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X, Y$ Distributions - Correlated') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(232)                                                   # annotated histogram of Y\n",
    "plt.hist(x=XY,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='green',density = True,label='$X + Y$')\n",
    "plt.vlines(np.average(XY),0,0.6,color='darkgreen',ls='--')\n",
    "plt.annotate('$E\\{X + Y\\}$ = ' + str(np.round(np.average(XY),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{X + Y}$ = ' + str(np.round(np.var(XY),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X, Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X + Y$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(233)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='blue',density = True,label='$Y$')\n",
    "plt.hist(x=XY,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='green',density = True,label='$X + Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod'); plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--');\n",
    "plt.vlines(np.average(XY),0,0.6,color='darkgreen',ls='--')\n",
    "plt.annotate('$\\sigma^2_{X+Y} = \\sigma^2_X + \\sigma^2_Y + 2 \\cdot C_{X,Y}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X,Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Y$, and $X + Y$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(234)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='grey',density = True,label='$Z$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$E\\{Z\\}$ = ' + str(np.round(np.average(Z),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.annotate('$s^2_{Z}$ = ' + str(np.round(np.var(Z),2)),(-4.5,0.31),fontsize = 13)\n",
    "plt.annotate(r'$C_{Z,X}$ = ' + str(np.round(np.cov(X,Z)[0][1],2)),(-4.5,0.24),fontsize = 13)\n",
    "plt.xlabel('$X,Z$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X, Z$ Distributions - Uncorrelated') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(235)                                                   # annotated histogram of Y\n",
    "plt.hist(x=XZ,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='$X + Z$')\n",
    "plt.vlines(np.average(XZ),0,0.6,color='darkgoldenrod',ls='--')\n",
    "plt.annotate('$E\\{X + Z\\}$ = ' + str(np.round(np.average(XZ),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{X + Z}$ = ' + str(np.round(np.var(XZ),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X, Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X + Z$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(236)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='grey',density = True,label='$Z$')\n",
    "plt.hist(x=XZ,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='$X + Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--');\n",
    "plt.vlines(np.average(XZ),0,0.6,color='darkgoldenrod',ls='--');\n",
    "plt.annotate('$E\\{X + Z\\} = E\\{X\\} + E\\{Z\\}$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$\\sigma^2_{X + Z} = \\sigma^2_X + \\sigma^2_Z + 2 \\cdot C_{X,Z}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X,Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Z$, and $X + Z$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.4, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69bc4856",
   "metadata": {},
   "source": [
    "The expected values for both cases are additive, this is general and holds if the random variables are correlated (e.g., $X$ and $Y$) or uncorrelated (e.g., $Z$ and $Y$).\n",
    "\n",
    "Also the variances are additive, the only difference is that we have to include the covaraince term, $2 \\cdot C_{X,Y}$, if there is correlation. \n",
    "\n",
    "That was addition of random variables, what about subtraction of random variables?\n",
    "\n",
    "#### Expectation of the subtraction of two random variables\n",
    "\n",
    "I demonstrate the following relationship for the addition of two random variables, $X$, and , $Y$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{X - Y\\} = E\\{X\\} - E\\{Y\\}\n",
    "\\end{equation}\n",
    "\n",
    "with expectation it can also be shown that the resulting variance will be:\n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_{X-Y} = \\sigma^2_X + \\sigma^2_Y - 2 \\cdot C_{X,Y} \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "47d46356",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "XY6 = X - Y                                                        # subtract 2 random variables\n",
    "XZ6 = X - Z\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(231)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='blue',density = True,label='$Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$E\\{Y\\}$ = ' + str(np.round(np.average(Y),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.annotate('$s^2_{Y}$ = ' + str(np.round(np.var(Y),2)),(-4.5,0.31),fontsize = 13)\n",
    "plt.annotate(r'$C_{X,Y}$ = ' + str(np.round(np.cov(R,rowvar=False)[0,1],2)),(-4.5,0.24),fontsize = 13)\n",
    "plt.xlabel('$X, Y$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X, Y$ Distributions - Correlated') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(232)                                                   # annotated histogram of Y\n",
    "plt.hist(x=XY6,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='green',density = True,label='$X - Y$')\n",
    "plt.vlines(np.average(XY6),0,0.6,color='darkgreen',ls='--')\n",
    "plt.annotate('$E\\{X - Y\\}$ = ' + str(np.round(np.average(XY6),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{X - Y}$ = ' + str(np.round(np.var(XY6),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X, Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X - Y$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(233)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Y,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='blue',density = True,label='$Y$')\n",
    "plt.hist(x=XY6,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='green',density = True,label='$X - Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Y),0,0.6,color='mediumblue',ls='--')\n",
    "plt.vlines(np.average(XY6),0,0.6,color='darkgreen',ls='--')\n",
    "plt.annotate('$E\\{X - Y\\} = E\\{X\\} - E\\{Y\\}$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$\\sigma^2_{X - Y} = \\sigma^2_X + \\sigma^2_Y - 2 \\cdot C_{X,Y}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X,Y$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Y$, and $X - Y$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(234)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='grey',density = True,label='$Z$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$E\\{Z\\}$ = ' + str(np.round(np.average(Z),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.annotate('$s^2_{Z}$ = ' + str(np.round(np.var(Z),2)),(-4.5,0.31),fontsize = 13)\n",
    "plt.annotate(r'$C_{Z,X}$ = ' + str(np.round(np.cov(X,Z)[0][1],2)),(-4.5,0.24),fontsize = 13)\n",
    "plt.xlabel('$X,Z$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X, Z$ Distributions - Uncorrelated') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(235)                                                   # annotated histogram of Y\n",
    "plt.hist(x=XZ6,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='$X - Z$')\n",
    "plt.vlines(np.average(XZ6),0,0.6,color='darkgoldenrod',ls='--')\n",
    "plt.annotate('$E\\{X - Z\\}$ = ' + str(np.round(np.average(XZ6),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{X - Z}$ = ' + str(np.round(np.var(XZ6),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X, Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X - Z$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(236)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='yellow',density = True,label='$X$')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='grey',density = True,label='$Z$')\n",
    "plt.hist(x=XZ6,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='$X - Y$')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.vlines(np.average(XZ6),0,0.6,color='darkgoldenrod',ls='--')\n",
    "plt.annotate('$E\\{X - Z\\} = E\\{X\\} - E\\{Z\\}$',(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$\\sigma^2_{X - Z} = \\sigma^2_X + \\sigma^2_Z - 2 \\cdot C_{X,Z}$',(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X,Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Z$, and $X - Z$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.4, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8166a7ef",
   "metadata": {},
   "source": [
    "#### Expectation of the product of two random variables \n",
    "\n",
    "I demonstrate the following relationship for the product of two random variables, $X$ and $Z$.\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{XZ\\} = E\\{X\\}E\\{Z\\}\n",
    "\\end{equation}\n",
    "\n",
    "Note, I only cover the case for two independent variables as this is required for this relation to hold.\n",
    "\n",
    "* there may be some departure from the result predicted from the analytical expression due to a small amount of correlation (not quite equal to 0.0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "59cca18b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ZX = Z * X                                                         # product of 2 independent random variables\n",
    "\n",
    "xmin = -5; xmax = 5; nbins = 30                                    # plotting parameters\n",
    "\n",
    "plt.subplot(131)                                                   # annotated histogram of X\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='yellow',density = True,label='X')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='grey',density = True,label='Z')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.annotate('$E\\{X\\}$ = ' + str(np.round(np.average(X),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_X$ = ' + str(np.round(np.var(X),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.annotate('$E\\{Z\\}$ = ' + str(np.round(np.average(Z),2)),(-4.5,0.38),fontsize = 13)\n",
    "plt.annotate('$s^2_{Z}$ = ' + str(np.round(np.var(Z),2)),(-4.5,0.31),fontsize = 13)\n",
    "plt.xlabel('$X$, $Z$'); plt.xlim([xmin,xmax]); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Z$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(132)                                                   # annotated histogram of Y\n",
    "plt.hist(x=ZX,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='XZ')\n",
    "plt.vlines(np.average(ZX),0,0.6,color='darkgoldenrod',ls='--')\n",
    "plt.annotate('$E\\{XZ\\}$ = ' + str(np.round(np.average(ZX),2)),(-4.5,0.52),fontsize = 13)\n",
    "plt.annotate('$s^2_{XZ}$ = ' + str(np.round(np.var(ZX),2)),(-4.5,0.45),fontsize = 13)\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X, Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$XZ$ Distribution') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplot(133)                                                   # annotated histogram of Y\n",
    "plt.hist(x=X,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='yellow',density = True,label='X')\n",
    "plt.hist(x=Z,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.1,edgecolor='black',color='grey',density = True,label='Z')\n",
    "plt.hist(x=ZX,weights=None,bins=np.linspace(xmin,xmax,nbins),alpha = 0.5,edgecolor='black',color='gold',density = True,label='XZ')\n",
    "plt.vlines(np.average(X),0,0.6,color='goldenrod',ls='--'); plt.vlines(np.average(Z),0,0.6,color='dimgrey',ls='--')\n",
    "plt.vlines(np.average(XZ6),0,0.6,color='darkgoldenrod',ls='--')\n",
    "plt.annotate('$E\\{XZ\\} = E\\{X\\}E\\{Z\\}$',(-4.5,0.52),fontsize = 13)\n",
    "\n",
    "plt.xlim([xmin,xmax]); plt.xlabel('$X,Z$'); plt.ylabel('Frequency'); plt.ylim([0,0.6]); plt.title('$X$, $Z$, and $XZ$ Distributions') \n",
    "plt.legend(loc='upper right')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=0.7, wspace=0.3, hspace=0.4); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cfa3584",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of statistical expectation operators. This concept is useful for many uncertainty modeling workflows, data science proofs, optimum decision making, etc., doing math with distributions!  \n",
    "\n",
    "Much more could be done, I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, geostatistics, machine learning and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
